Method of estimating the volumetric carrying capacity of a truck body

ABSTRACT

A method for estimating the effective volumetric capacity of a truck body includes establishing a side-to-side profile of a generic load model by extending load side lines upward at a predetermined material angle of repose from the upper edge of the side walls of the truck body and a front-to-rear profile by extending a front load line upward from the upper edge of the front wall and a rear load line upward from at or near a rear edge of the floor at the predetermined material angle of repose. Load plateau lines having predetermined dimensions are established and the height of the plateau lines is determined. A top pro of the generic load is then created and the shape of the load plateau is adjusted into a closed curve shape. A final three-dimensional generic load model is formed and the volume of the load model is calculated.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This patent application claims the benefit of U.S. Provisional Patent Application No. 60/336,064, filed Nov. 2, 2002.

FIELD OF THE INVENTION

This invention relates generally to off-highway trucks and more particularly to a method of calculating the estimated volumetric carrying capacity of the body of an off-highway truck.

BACKGROUND OF THE INVENTION

In mining and construction environments, off-highway trucks are used to haul a variety of different materials such as, for example, coal, rock, ore and overburden materials (i.e. the material overlying ore/coal deposits). Such off-highway trucks generally comprise a truck chassis or frame, which supports a truck body for receiving and carrying a load.

The carrying capacity of a truck is defined by two parameters: the weight or load carrying capacity of the truck and the volumetric carrying capacity of the truck body. These two parameters must be synchronized with the density of the material to be carried by the truck to ensure that the truck is properly utilized. If not, the truck can be operating either under capacity, i.e. short in payload, or over capacity, i.e. with a heavier than desired payload.

The truck manufacturer defines the weight carrying capacity of an off-highway truck. For a given haulage application, dividing the truck weight carrying capacity by the density of the material to be carried yields the required optimal volumetric carrying capacity for the truck body in that application.

Presently, off-highway truck manufacturers provide a volumetric capacity rating for their truck bodies that is presently based on the Society of Automotive Engineers (SAE) Standard SAE J1363 (January 1985, reaffirmed November 1995) (“the SAE standard”). Unfortunately, however, this SAE standard does not provide a very accurate estimate of the actual volumetric carrying capacity of a truck body.

The SAE standard rates the volumetric capacity of a truck body both in struck and heaped volumetric capacities. The sum of its struck volume and its 2:1 heap above the struck volume/struck line is its 2.:1 heaped volume. Under the SAE standard, the struck volume of large off-highway truck dump bodies is based on an assumed struck load which extends upward from the rear edge of the floor of the truck body (on open ended truck bodies) at a 1:1 slope (corresponding to a material angle of repose of 45 degrees) to the top edge of the side walls of the body. The heaped volume is based on an assumed load heap defined by the truck body sides and the line defined by the intersection of the rear struck line and the body sides and extends upwards at a 2:1 slope (corresponding to an angle of repose of 26.6 degrees).

There are major dimensional problems with the SAE 2:1 heaped volumetric rating methodology set forth in the SAE standard. First, with respect to the struck volume calculation, there are very few materials that will stand at a 1:1 slope in a static condition let alone in a dynamic condition, i.e. when the truck is moving. Second, the heaped volume calculation is based on a different slope or material angle of repose than is used in calculating the struck volume. Thus, the SAE standard essentially assumes a load that does not have a constant material angle of repose, i.e. a load wherein the angle of repose of the load material at the rear of the truck body changes from 45 degrees to 26.6 degrees above the side walls of the truck body. In the real world, each particular side of a load heap carried in a truck body nearly always has a substantially constant angle of repose. However, it should be noted, that each side of a load heap, i.e. front, back, left a d right may not always have the same angle of repose.

The third major problem with the methodology of the SAE standard is that it attempts to define the load heap by a series of four flat planes, which together resemble the roof of a house. In actuality, load heaps carried in truck bodies have a configuration that is more conical in shape.

Accordingly, the methodology of the SAE standard is based on a load model that is different in several critical respects from the actual real world configuration of a load carried by a truck body. As a result, the SAE standard produces a truck body volumetric capacity rating drat does not accurately reflect the actual achievable volumetric carrying capacity of a truck body. In fact, the SAE standard consistently overrates the volumetric carrying capacity of a truck body. This is recognized in certain South American countries where the practice is to “de-rate” the SAE standard volumetric capacity of a truck body to 85% of the volumetric rating produced by the SAE standard. This method, however, also provides little more than a rough estimate of the actual volumetric carrying capacity of a truck body.

Since the SAE standard substantially overrates the actual volumetric weight carrying capacity of a truck body, off-highway truck users typically are unable to achieve the full load-carrying capabilities of their truck. Moreover, attempts to match the effective volumetric carrying capacity of a truck body with the materials being hauled and the weight carrying capacity of the truck so as to achieve full payload utilization of the truck amount to little more than guesswork because of the inaccuracy of the SAE standard. Accordingly, a need exists for a method to accurately estimate the effective volumetric carrying capacity of a truck body.

BRIEF SUMMARY OF THE INVENTION

The invention provides a method for rating or estimating the effective volumetric carrying capacity of a truck body. The method includes a Step A where a side-to-side profile of a generic load model is established by extending load side lines upward at a predetermined material angle of repose from the upper edge of each of the side walls of the truck body. In Step B, a front-to-rear profile of the generic load model is established by extending a front load line upward from the upper edge of the front wall of the truck body at the predetermined material angle of repose and a rear load line upward from at or near a rear edge of the floor of the truck body at the predetermined material angle of repose. Step C consists of defining a load plateau plane having predetermined dimensions in the front-to-rear and side-to-side profiles and determining the height of the load plateau plane. In Step D, the top profile of the generic load is then created from the side-to-side and front-to-rear profiles and the shape of the load plateau is then adjusted into a closed curve shape. In step E, the front, rear and side load lines below the final outer boundary of the load plateau are contoured into a generally conically shaped surface in which the sides of the conically shaped surface are inclined at the predetermined material angle of repose. This forms a final three-dimensional generic load model defined by the load plateau and where the generally conically shaped surface intersects the side wails, front wall and floor of the truck body. In Step F, the volume of the final three-dimensional generic load model is calculated.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side view of an exemplary off-highway truck having a truck body the capacity of which can be rated using the method of the present invention.

FIG. 2 is a rear view of the off-highway truck of FIG. 1.

FIG. 2 a is a diagram representing exemplary material angles of repose with corresponding material slopes of 2.2:1-1.4:1.

FIG. 3 is an end view of the truck body showing a step in establishing a side-to-side profile of a generic load in accordance with the present invention.

FIG. 4 is an end view of the truck body showing a further step in establishing the side-to-side profile of the generic load that includes establishing a side-to-side profile of the load plateau plane.

FIG. 5 is a side view of the truck body showing a step establishing a front-to-rear profile of the generic load.

FIG. 6 is a side view of the truck body showing a further step in establishing the front-to-rear profile of the generic load that includes establishing a front-to-rear profile of the load plateau plane.

FIG. 7 is a side view of the truck body showing the difference in height between t front-to-rear profile of the load plateau plane and the side-to-side profile of the load plateau plane.

FIG. 8 is a side view of the truck body showing the final front-to-rear profile of the generic load.

FIG. 9 is an end view of the truck body showing the final side-to-side profile of the generic load.

FIG. 10 is a top view of the truck body and generic load showing how the load plateau plane is transformed into a generally circular or oval shaped load plateau.

FIG. 11 is a top view of the truck. body and the generic load showing how the load. plateau can be divided into pie-shaped segments.

FIG. 12 is a perspective view of the truck body and the generic load showing how the load profile lines are extended from the load plateau to the inside surface of the truck body.

FIG. 13 is a perspective view of the truck body and the generic load model showing how the lines of contact between the generic load and the inside surface of the truck body are defined.

FIG. 14 is a perspective view of the truck body and the generic load model.

FIGS. 15 a, b, and c are comparison diagrams showing the difference between the truck body volumetric capacity rating as calculated in accordance with the present invention (FIG. 15 a) and the rating based on a true 2:1 heap (FIG. 15 b) and the SAE volumetric capacity rating (FIG. 15 c).

FIG. 16 is a perspective view of a truck body having sideboards showing how the addition of the sideboards affect the volumetric carrying capacity rating of the truck body as calculated according to the present invention.

FIG. 17 is a perspective view of a truck body having a tail extension showing how the addition of the tail extension affects the volumetric carrying capacity rating of the truck body as calculated according to the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Referring now more particularly to the drawings, there is shown in FIGS. 1 and 2 an exemplary off-highway truck 10 having a body 12 the volumetric capacity of which can be rated according to the method of the present invention. The truck 10 includes a chassis 14 to which the body 12 is attached. The chassis 14, in turn, is supported by a plurality of tires 16. The truck body 12 is generally constructed of steel panels which define the shape of the body 12 and beams which form the structural framework for the body 12. The truck body 12 comprises, in this case, side walls 18, a front wall 20 or front slope and a floor 22. It will be appreciated, however, that the method of the present invention can he used on truck bodies having any suitable configuration.

In the illustrated embodiment, the truck 10 and truck body 12 are generally symmetrical about their longitudinal axes. Accordingly, as will be appreciated, reference to plural elements where only one is shown indicates that a complementary element is disposed on the side of the truck not shown (e.g., side walls 18).

In accordance with the present invention, a method is provided for much more accurately calculating or rating the volumetric carrying capacity of a truck body. In particular, the method of the present invention provides a volumetric carrying capacity rating which much more closely approximates the actual achievable effective volumetric carrying capacity of the truck body under real-life loading conditions than the volumetric rating produced using the SAE standard methodology and other similar methodologies. Thus, the present invention allows off-highway truck end users to more easily evaluate and select truck bodies for their particular haulage application. This, in turn, leads to more efficient truck utilization, i.e. trucks carrying loads more closely matched to their volumetric and weight carrying capacity.

Step 1—Establishing the Material Angle of Repose

As a first step for determining an effective volumetric capacity rating for a particular truck body, the truck body 12 in the illustrated embodiment, an assumption has to be made with regard to the load material angle of repose α. Any suitable value can be used such as illustrated in FIG. 2 a. For example, in the illustrated embodiment, a 26.6 degree angle of repose α, which corresponds to a 2:1 load heap, is used for the load heap “around” the truck body 12.

While a constant angle of repose α, is used in the illustrated embodiment for ease of calculation, different angles of repose for the front, rear and sides of the load often occur. A method of designing truck bodies that can include collecting specific angle of repose data from a specific site is disclosed in copending application Ser. No. 09/333,379.

Similarly, the predetermined angle of repose α used in the method of the present invention can be based on observations of loads carried by truck bodies in the field. In such a case, the material angle of repose in the dynamic condition should be Observed. Accordingly, the material angle of repose should be observed after the truck has been driven a reasonable distance and the load has stabilized.

In order to provide standard uniformity in the volumetric capacity ratings calculated according to the present invention, it may be advantageous to use a standard material angle of repose α for all calculations. Alternatively, a set of standard values may be employed with each individual standard value corresponding to a particular application (e.g., coal mine, copper mine, iron mine, etc.). Thus, when rating the volumetric capacity of a body for a particular application, the corresponding standard material angle of repose α for such material could be used. Typical angles of repose are indicated in FIG. 2 a.

Step 2—Establishing Side-to-Side Profile of Generic Load

After establishing the material angle of repose α to be used, a dimensional-dimensional model of a generic load 25 (FIGS. 8, 9, 10, 11, 13, 14, 16, 17) carried by the truck body 12 is created. This generic load model 25 is preferably created using a three-dimensional solids computer aided design (CAD) system for ease of calculation. However, the present invention is not limited to being performed with CAD systems and could be performed using other systems and methods. In the illustrated embodiment, the three-dimensional generic load model 25 is begun by creating an initial side-to-side profile 24 (FIG. 3) of the generic load model 25. in particular, a load side line 26 is extended upward from the upper edge or upper inner edge of each of the side walls 18 at the predetermined angle of repose α (e.g., 26.6 degrees) to a peak in the middle using an end view of the body 12 as shown in FIG. 3.

In reality, material carried in a dump body is rarely loaded to a perfect peak, rather a horizontally extending plateau forms on the top of the heaped load. Thus, a side-to-side profile 28 (FIG. 4) of the load plateau is next formed with a predetermined width WE in the side-to-side profile 24 of the generic load model 25 as shown in FIG. 4. In this case, the width WE of the side-to-side plateau profile line 28 is set at ⅕^(th) of the inside width of the truck body 12, however, any suitable value, i.e. ¼, ⅙, 1/7, ⅛, 1/9, can be used. In creating the side-to-side plateau profile line 28, the side load lines 26 of the generic load model 25 are maintained at the predetermined angle of repose α and the load peak is removed above the side-to-side plateau profile line 28, i.e. the line where the horizontal distance between the side load lines equals the predetermined width WE of the side-to-side plateau profile line 28.

Step 3—Establishing Front-to-Rear Profile of Generic Load

In the illustrated embodiment, as a next step, a front-to-rear profile 30 (FIG. 6) of the generic load model 25 is produced. Specifically, using a side view of the truck body 12, a front load line 32 is extended upward (FIG. 5) from the upper edge of the front body slope 20 at the predetermined material angle of repose α as shown in FIG. 5. Similarly, a rear load line 34 is extended upward (FIG. 6) from the rear edge of the floor 22. of the truck body 12 at the (predetermined angle of repose α until it intersects the front load plane 32 (shown in phantom in FIG. 6). In order to take into account the possibility that loading of the rear of the body 12 to a spill point is unacceptable because of the possibility of spillage out of the rear end of the body onto a haul road, the rear load line 34 can be extended upward from a point spaced a distance D (e.g., 6 inches) inward from the rear edge of the floor 22 as shown in FIG. 6.

After the front and rear load lines 32, 34 are established, a front-to-rear profile 36 of the load plateau is then created (FIG. 6) with a predetermined length LS on the peak of the intersecting front and rear load lines 32, 34 as shown in FIG. 6. In this case, the front-to-rear plateau profile line 36 has a length LS equal to the width WE used in creating the side-to-side plateau profit- line 28 (i.e., the step illustrated in FIG. 4). As in step 2, the angle of repose α is kept constant in creating the front-to-rear plateau profile line 36.

Step 4—Determining Maximum Height of Generic Load Model

As a next step, the maximum height of the generic load model 25 is determined. This is accomplished by comparing the height HE of the side-to-side plateau profile line 28 and the height HS front-to-rear plateau profile line 36, such as shown in FIG. 7. Specifically, the final height HF (FIG. 8) of the generic load model 25 is set at the lower of the height HE of the side-to-side plateau profile line 28 and the height HS of the front-to-rear plateau profile line 36 (assuming that these two heights are different). The lower height is used because the height of an actual load in the body 12 will be limited by either the length or width of the body (unless such as in ideal situations HS equals HE). For example, in the illustrated embodiment HE exceeds HS. The true height of an actual load will not reach HE because the body 12 is not long enough at the chosen material angle of repose u to hold a load of that size.

Once the final height HF is determined, both the side-to-side and front-to-rear plateau profiles 28, 36 are set at the final height HF above the body sides 18 (FIGS. 8 and 9 respectively). In particular, the height of the plateau line in the profile (front-to-rear or side-to-side) having the higher height above the body side 18 is lowered to the height of the lower plateau line. Thus, at this point, the plateau lines should be at the final height HF in both the side-to-side and front-to-rear profiles 24, 30 of the generic load model 25 as shown in FIGS. 8 and 9. In the profile in which the height of the plateau line was lowered, the plateau line will be longer than the predetermined distance used to initially define the plateau WE will no longer equal LS) because the material angle of repose α of the side, front and rear load lines 26, 32, 34 remains constant.

Note that the plateau width WE should not be more than 20% larger than the original width established in Step 2. While load heaps can easily run the length of the body, load heaps running the width of the truck body are seldom if ever achievable, If the plateau width WE does exceed the original width by more than 20% it will indicate that the point where the load contacts the body side walls 18 is below the top of the side walls 18 or that the angle of repose for the material running to the body sides is less than that established in Step 1, i.e. the loading tool has to artificially push material sideways to get material to reach the top of the body side wails. When designing a body, this problem can be corrected by lengthening the body in the front-to-rear view or profile.

It will be appreciated that the steps 2 and 3 described above and illustrated in FIGS. 3-7 do not have to be performed in any particular order so long as side-to-side and front-to-rear profiles 24, 30 of the generic load model 25 are established and the height and length of the load plateau lines are defined. For example, the front-to-rear profile 30 of the generic load model 25 can be produced prior to the side-to-side profile 24.

Step 5—Defining Shape of Load Plateau

At this stage, the side, front and rear load lines 26, 32, 34 and the load plateau lines 28, 36 define the generic load model 25. In order to more accurately reflect the shape of an actual load heap carried in a truck body 12, the generic load model 25 is next molded into a more conical shape. In the illustrated embodiment, this is accomplished by first creating a top load plateau profile 40 which in most cases will be oblong in nature though it could also be round if HS and HE are the same height. As shown in FIG. 10, the load plateau as defined by the side-to-side and front-to-rear profile lines initially has a rectangular shape when viewed from the top (because WE no longer equals LS). To more accurately reflect the shape of an actual load plateau, this rectangular shape must be converted into a rounder oblong or oval shape. In this case, the final top load plateau profile 40 is produced by inscribing an oval or circle within the lines of the rectangle. This oval or circle becomes the outer boundary of the load plateau 38.

Step 6—Contouring Generic Load to Produce a More Conical Shape

Using the oval shaped top profile 40 of the load plateau 38 as the starting point, the side, front and rear load lines 26, 32, 34 of the generic load r yodel 25 produced in creating the side-to-side and front-to-rear profiles 24, 30 of the generic load model 25 are contoured so that the generic load model 25 more closely resembles a conical shape. In this case, the oval shaped load plateau top profile 40 is divided into a plurality of pie-shaped increments by boundary lines 42 as shown in FIG. 11. The boundary lines 42. defining the pie shaped increments are spaced at equal angular intervals. In the illustrated embodiment, the load plateau 38 is divided into thirty-six 10 degree pie-shaped segments. Since it is anticipated that an actual load will be symmetrical about the centerline of the body 12, the load plateau 38 could be divided in increments 42 only to one side of the body 12 (e.g., eighteen 10 degree increments). The opposite side of the generic load model 25 would then be formed as a mirror image of the side divided into increments.

For each pie-shaped segment boundary line 42, a contour line 44 (FIG. 12) is extended downward at the predetermined material angle of repose α from the edge of the oval-shaped plateau 38 perpendicular to the tangent line of the plateau 38 at that point until the contour line 44 intersects the inside surface of the truck body 12 as shown in FIG. 12. To define the lines of contact between the generic load model 25 and the sidewalk 18, front slope 20 and floor 22 of the body 12, the points where the contour lines 44 contact the inside of the truck body 12 are connected to form a series of contact line segments 46 as shown in FIG. 13. The upper surface of the load model 25 is then formed (FIG. 14) by extending a contour plane 48 between each adjacent pair of the contour lines 44 from the plateau to the respective body contact line segment 46. These contour planes 48 shape the upper surface of the generic load model 25 into a generally conical shape as shown in FIG. 14.

Step 7—Determine Volumetric Capacity Rating

The volume of the three-dimensional generic load model 25 is then calculated. This volume represents the effective volumetric carrying capacity of the truck body 12. The volume of the dimensional-dimensional generic load model 25 is most easily calculated using a CAD system. However, it is conceivable that the volume could be calculated using other methods,

An example of the significant difference between the effective volumetric capacity rating as calculated using the method of the present invention and the capacity rating calculated using conventional methods is illustrated in FIGS. 15 a-c. In particular, three dimensionally identically sized truck bodies are illustrated in FIGS. 15 a-c. The effective volumetric capacity of the first truck body 50 (FIG. 15 a) has been rated using the method of the present invention. The volumetric capacity of the second truck body 52 (FIG. 15 b) has been rated based on a load model using only a 2:1 heap (i.e., where the 2:1 slope is maintained from the floor edge at th rear of the body) and flat planes. Finally, the volumetric capacity of the third truck body 54 (FIG. 15 c) has been rated based on the method set forth in the SAE standard. As can be seen from FIG. 15, the volumetric capacity rating produced using the present invention (FIG. 15 a) is approximately 18% less that the rating produced using the SAE standard (FIG. 15 e) and approximately 11% less than the rating produced using a true 2:1 heap (FIG. 15 b).

In order to maximize the volumetric load carrying capacity of a truck body 12, the height of the side walls 18 and the length of the body 12 must also be properly matched. This becomes evident when the method of the present invention is used to rate the volumetric carrying capacity of a truck body 12 which has been modified with sideboards 56 or a tail extension 58. For example, FIG. 16 illustrates a completed generic load model 25 that has been produced using the method of the present invention for a truck body 12 having sideboards 56. The sideboards 56 increase the height of the side walls 18 of the body 12, however, they can not be fully utilized because the volumetric capacity of the body 12 is limited by the length of the floor 22 which has been kept constant. In particular, when performing steps 2-4 (FIGS. 3-10) of the present invention, the height HS (FIG. 6) of the front-to-rear plateau profile line 36 (which takes into account the length of the floor) is lower than the height HE (FIG. 4) of the side-to-side plateau profile line 28 (which takes into account the height of the side walls 18 plus the sideboards 56). Thus, the side-to-side plateau profile line 28 (FIG. 4) must be lowered to correspond to the height HS of the front-to-rear plateau profile line 36 (FIG. 6), thereby limiting the effectiveness of the sideboards 56 with regard to increasing the volumetric carrying capacity of the truck body 12.

The opposite is true if the truck body 12 is lengthened, such as by using a tail extension 58, while the side walls 18 are kept at the same height such as shown in FIG. 17. Specifically, in such a case the height of the side walls 18 limits the volumetric carrying capacity of the truck body 12 because the height HE of the side-to-side plateau profile line 28 is lower than the height HS of the front-to-rear plateau profile line 36. This fact can be compensated some by lengthening the length of the final load plateau 38, however the typical problem with lengthening the final load plateau is that the center of gravity of the load model 25 is shifted rearward which may create an out of balance condition relative to the truck that is carrying the truck body and in lengthening the rear of the truck body the ground clearance of the truck body when dumped may be below the minimum required by statutory guidelines. Typical statutory regulations require that when dumped the rear lower corner of the truck body be no lower than the centerline of the axle of the truck on which the dump body is mounted. Otherwise, the height of the load plateau line has to be lowered in the front-to-rear profile thereby limiting the extra volumetric carrying capacity and limiting the length of the tail extension 58.

All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein.

The use of the terms “a” and “an” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention.

Preferred embodiments f this invention are described herein, including the best mode known to the inventor for carrying out the invention. Of course, variations of those (preferred embodiments will become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventor expects skilled artisans to employ such variations as appropriate, and the inventor intends for the invention to be practiced otherwise than as specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context. 

1-7. (canceled)
 8. A method for estimating the volumetric capacity of an off-highway truck body design having a pair of side walls, a front wall and a floor, comprising the steps of: determining at east one material angle of repose of a heaped load to be carried by the truck body; establishing a three-dimensional model of the heaped load having a substantially conical upper surface that is based on the at least one material angle of repose and that intersects portions of the side walls, front wall and floor of the truck body design; and calculating a volume of the three-dimensional model of the heaped load.
 9. The method of claim 8 wherein the shape of the load is different for differently shaped truck body designs but the upper conical surface of the heaped load is similar.
 10. The method of claim 8 wherein the establishing the three-dimensional model of the heaped load includes determining a height of a top load plateau profile of the three-dimensional model based on dimensions of the truck body design.
 11. The method of claim 8, wherein the material angle of repose is determined by observing loads carried by truck bodies in the field.
 12. The method of claim 8, wherein the truck body design has an open rear end.
 13. The method of claim 8, wherein the (rack body design includes an open top. 